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Properties

Label 25410.2.a.ek
Level $25410$
Weight $2$
Character orbit 25410.a
Self dual yes
Analytic conductor $202.900$
Dimension $3$

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Show commands: Magma / Pari/GP / SageMath

Newspace parameters

Copy content comment:Compute space of new eigenforms
 
Copy content gp:[N,k,chi] = [25410,2,Mod(1,25410)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)
 
Copy content magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("25410.1"); S:= CuspForms(chi, 2); N := Newforms(S);
 
Copy content sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(25410, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([0, 0, 0, 0])) N = Newforms(chi, 2, names="a")
 
Level: \( N \) \(=\) \( 25410 = 2 \cdot 3 \cdot 5 \cdot 7 \cdot 11^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 25410.a (trivial)

Newform invariants

Copy content comment:select newform
 
Copy content sage:traces = [3,-3,-3,3,-3,3,3,-3,3,3,0,-3,-4,-3,3,3,-1,-3,5,-3,-3,0,2,3,3, 4,-3,3,-2,-3,4,-3,0,1,-3,3,-2,-5,4,3,4,3,-1,0,-3,-2,-18,-3,3,-3,1,-4,-7, 3,0,-3,-5,2,-3,3,9,-4,3,3,4,0,7,-1,-2,3,-1,-3,13,2,-3,5,0,-4,-13,-3,3, -4,12,-3,1,1,2,0,10,3,-4,2,-4,18,-5,3,-3,-3,0,3] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(None)] == traces)
 
Copy content gp:f = lf[1] \\ Warning: the index may be different
 
Self dual: yes
Analytic conductor: \(202.899871536\)
Dimension: \(3\)
Coefficient field: 3.3.2636.1
Copy content comment:defining polynomial
 
Copy content gp:f.mod \\ as an extension of the character field
 
Defining polynomial: \( x^{3} - 14x - 4 \) Copy content Toggle raw display
Twist minimal: not computed
Fricke sign: \(+1\)
Sato-Tate group: $\mathrm{SU}(2)$

$q$-expansion

The algebraic \(q\)-expansion of this newform has not been computed, but we have computed the trace expansion.

\(\operatorname{Tr}(f)(q) = \) \( 3 q - 3 q^{2} - 3 q^{3} + 3 q^{4} - 3 q^{5} + 3 q^{6} + 3 q^{7} - 3 q^{8} + 3 q^{9} + 3 q^{10} - 3 q^{12} - 4 q^{13} - 3 q^{14} + 3 q^{15} + 3 q^{16} - q^{17} - 3 q^{18} + 5 q^{19} - 3 q^{20} - 3 q^{21}+ \cdots - 3 q^{98}+O(q^{100}) \) Copy content Toggle raw display

Atkin-Lehner signs

\( p \) Sign
\(2\) \( +1 \)
\(3\) \( +1 \)
\(5\) \( +1 \)
\(7\) \( -1 \)
\(11\) \( -1 \)

Inner twists

Inner twists of this newform have not been computed.

Twists

Twists of this newform have not been computed.